1. **State the problem:** We need to identify which lists contain only irrational numbers. 2. **Recall definitions:** - Rational numbers can be expressed as a fraction of two integers. - Irrational numbers cannot be expressed as such fractions. - Square roots of non-perfect squares are irrational. - Square roots of perfect squares are rational. 3. **Analyze each list:** - List 1: -11.8, -7.3, -9.7, -3, 61.4 These are decimal numbers and integers. Decimals like -11.8, -7.3, -9.7, and 61.4 are terminating decimals, which are rational. -3 is an integer, also rational. So this list contains only rational numbers. - List 2: \(\sqrt{20}, \sqrt{50}, \sqrt{35}, \sqrt{65}, \sqrt{70}\) All these are square roots of non-perfect squares, so all are irrational. - List 3: \(\frac{21}{22}, \frac{3}{11}, \frac{1}{9}, -\frac{2}{5}, -\frac{1}{17}\) All are fractions of integers, so all rational. - List 4: \(\sqrt{25}, \sqrt{81}, \sqrt{36}, \sqrt{144}, \sqrt{100}\) These are square roots of perfect squares: 5, 9, 6, 12, 10 respectively, all rational. - List 5: \(2\sqrt{2}, 5\sqrt{5}, 3\sqrt{3}, 6\sqrt{6}, 7\sqrt{7}\) Each is a rational multiple of an irrational number (square root of non-perfect square), so all irrational. 4. **Final answer:** Lists 2 and 5 contain only irrational numbers.